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Abstract
In this paper, a modified low-bandwidth sub-Nyquist sampling receiving scheme enabled by optical shaping is investigated in an intensity modulation/direct detection (IM/DD) orthogonal frequency-division multiplexing (OFDM) system, which can reduce the sampling rate and analog bandwidth of an analog-to-digital converter (ADC) at the receiving end. By changing the phase matrix of preprocessing, the modified scheme can distinguish different groups of data only by controlling the delay of the shaping module. In addition, the proposed RF sharing architecture can further reduce the cost and increase the feasibility of the scheme. Based on arcsine digital pre-distortion (DPD) technology, a DPD optical pulse shaping scheme is proposed to achieve better spectrum aliasing in the optical domain. With the help of the DPD shaping, we successfully experimentally demonstrate the 12.5-GHz/44.45-Gbit/s IM/DD OFDM system with low-bandwidth (3.125 GHz) and sub-Nyquist sampling rate (6.25 GSa/s) ADC. The experiment results show that the proposed scheme can not only effectively achieve low-bandwidth reception, but also achieve about 0.4 dB receiver sensitivity improvement compared with the traditional high-bandwidth scheme at BER of 3.8×10−3 after 10.2 km standard single mode fiber transmission, which indicates that the proposed scheme is a promising low-cost candidate to provide large transmission capacity for the next-generation network.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
With the continuous growth of emerging technologies, such as virtual reality (VR), cloud computing, and peer-to-peer multimedia services, the bandwidth demand for optical communication systems has been constantly booming [1–3]. To meet the growing demand, intensity modulation/direct detection (IM/DD) optical transmission system is considered an attractive and feasible solution in terms of system cost, complexity and power consumption [4–7]. Many advanced modulation formats are widely studied in the IM/DD system, such as carrier-less amplitude/phase modulation (CAP), pulse amplitude modulation (PAM) and orthogonal frequency-division multiplexing (OFDM) [8]. Among all the advanced modulation formats, OFDM stands out from them because of its dynamic bandwidth allocation, high spectral efficiency and dispersion tolerance [9,10]. Therefore, IM/DD OFDM system can be applied to point to multi-point (P2MP) networks such as passive optical network (PON), beyond 5G and 6G fronthaul (B5G/6G FH) and radio-over-fiber (RoF) [11–13].
In such a P2MP OFDM system, multiple receivers are connected to a transmitter. Thus, the aggregated downstream OFDM data rate will be very high. According to the Nyquist sampling theorem, the sampling rate of the analog-to-digital converter (ADC) at each receiver is supposed to be high enough to process the aggregated OFDM data, even though only a small portion of downstream data is needed [14], which leads to the redundancy in data reception. In the literature, several different schemes are proposed to increase the data rate while reducing the ADC’s sampling rate. It can be categorized into the following two types: 1) Multi-band transmission: multiple OFDM signals are frequency division multiplexed (FDM) in the electrical domain, thus increasing the total data rate of the system and reducing the requirements of the digital-to-analog converter (DAC) /ADC sampling rate of the sub-band system [15–17]. However, the mixer and precise oscillator should be equipped for up-conversion/down-conversion at the transmitter/receiver side in these schemes. In addition, the up-conversion can also be realized by return-to-zero (RTZ) DAC and analog high-pass filter (HPF) [18]. But in general, the multi-band scheme requires additional analog circuits, which will increase the complexity of the system and the difficulty of maintenance. 2) Sub-Nyquist sampling reception: a sub-Nyquist sampling receiving scheme employing channel-characteristic-division multiplexing (CCDM) is proposed to reduce the sampling rate of ADC [19,20]. Different electrical filters are placed in front of the ADCs to provide unique channel characteristics for receivers [19]. By preprocessing the aggregated OFDM signal at the transmitter, the system allows a receiver to detect the demanded data after corresponding channel transmission and spectral aliasing caused by sub-Nyquist sampling. As a special form of CCDM, the delay-division multiplexing (DDM) scheme distinguishes the channel phase response by controlling the sampling delay of the ADC [21–24].
Nevertheless, the traditional DDM scheme [21] reduces the requirement of ADC sampling rate but neglects the reduction of the analog bandwidth of ADC, because all transmitted subcarriers must be reserved before the spectrum aliasing caused by sub-Nyquist sampling. Thus, an optical shaping technique based on Mach-Zehnder modulator (MZM) is proposed to reduce the required analog bandwidth of ADC in a DDM-based OFDM system [25]. The core idea of this technology is to utilize optical shaping pulse to equivalently achieve spectral aliasing in the optical domain. Different optical shaping pulses are also studied in [25], which will directly affect the transmission performance. However, the study does not mention how to achieve better optical shaping, and the delay multiplexing method is redundant because the preprocessing matrix is the same as the traditional scheme.
This paper is an extension of our early work [26], in which the arcsine digital pre-distortion shaping (DPD) technique is proposed to improve optical shaping. The simulation results showed that the improved scheme could achieve better transmission performance than the scheme in [25]. However, the work was completed in the simulation platform without considering the feasibility of the actual experiment. In this paper, we propose a modified low-bandwidth sub-Nyquist sampling receiving scheme based on DPD shaping (called modified low-bandwidth DDM scheme). By changing the phase matrix of preprocessing, each group only needs to precisely control the delay of the shaping module to receive the corresponding data. The RF sharing architecture is also proposed to reduce the cost and increase the feasibility of the scheme. With the DPD shaping, the modified low-bandwidth DDM scheme can obtain a flatter magnitude response, which is conducive to improving transmission performance. An optical band-pass filter (OBPF) placed at the receiver is not only used to minimize the out-of-band amplified spontaneous emission (ASE) noise but also to suppress subcarrier-to-subcarrier beating interference (SSBI) introduced by optical shaping pulse harmonics. In addition, we experimentally demonstrate the 12.5-GHz/44.45-Gb/s DDM-based OFDM system employing low-bandwidth (3.125 GHz) and sub-Nyquist sampling rate (6.25 GSa/s) ADC. The experiment results prove that the modified low-bandwidth DDM scheme can achieve about 0.4 dB receiver sensitivity improvement compared with the traditional high-bandwidth DDM scheme at the hard decision forward error correction (HD-FEC) threshold (3.8×10−3) after 10.2 km standard single mode fiber (SSMF) transmission.
The rest of this paper is organized as follows. Section 2 presents the principle of the modified low-bandwidth DDM scheme. Section 3 describes the experiment setup. Section 4 illustrates the discussion of experimental results. Finally, our work is summarized in Section 5.
2. Operation principle
2.1 Concept of modified low-bandwidth DDM scheme
According to the principle of the traditional DDM scheme [21] based on sub-Nyquist sampling, if the FFT size of the transmitter is N and the receiving end has M (M should be the power of 2) virtual groups, each group only requires a 1/M Nyquist sampling rate and N/M fast-Fourier transform (FFT) size in demodulation. Based on the predictable spectral aliasing mode and corresponding preprocessing at the transmitter, each group can receive its requested data. The procedure of transmission and aliasing can theoretically be written as follows:
${\bf T}$ represents the data subcarrier in the frequency domain of the transmitter. ${\bf R}$ indicates the received data aggregated from all groups, and ${\bf H}$ describes the transmission response of different data subcarriers, including the impact of spectral aliasing [21]. Therefore, when the transmitter preprocesses the signal as follows: where ${{\bf H}^{\textrm{ - 1}}}$ is the inverse of ${\bf H}$, so that each group can receive the expected signal after the corresponding transmission and spectral aliasing [22]. The process can be given by:Additionally, assuming the channel characteristics of all groups are similar before A/D conversion, the traditional DDM scheme generates different transmitted subcarriers by the use of different sampling delays. Different delays will produce different phase shifts in the frequency domain, such that the received subcarriers from different groups will be different linear combinations of transmitted subcarriers. However, the traditional scheme reduces the sampling rate of ADC but doesn’t decrease its analog bandwidth. The concept of low-bandwidth DDM scheme employing optical shaping is to perform spectral aliasing before photoelectric conversion, which can reduce the analog bandwidth of the receiver to 1/M [25].
Nevertheless, if the traditional preprocessing method [21] is used directly, the low-bandwidth DDM scheme requires different groups to receive the corresponding data by controlling the delay of shaping and sampling instant [25]. Therefore, each receiver would have two devices requiring precise delay control. To further increase the feasibility, we propose a modified delay multiplexing method by changing the phase matrix, which is more suitable for low-bandwidth DDM schemes. The modified ${\bf H}$ can be written as:
In this modified delay multiplexing method, the phase rotation factor ${e^{j\frac{\textrm{N}}{{2\textrm{M}}}{\omega _0}\Delta t}}$ is generated by the delay of optical shaping module. Thus, each group is only assigned a specific shaping delay to receive the corresponding data and is not sensitive to the sampling instant because it can use TSs for phase compensation. It is worth mentioning that the transmission performance of DDM scheme is determined by the condition number of the matrix ${\bf H}$, which indicates the sensitivity of the matrix calculation to errors [27]. When the condition number is larger, the numerical stability of the matrix is worse, and the matrix is closer to the singular matrix. According to Ref. [27] and experimental results, the condition number less than 6 is acceptable. The modified phase matrix is still a unitary matrix, which is equivalent to the traditional matrix.
According to the previous discussion, the shaping modules of each group differ only in shaping delay. To further reduce system cost and complexity, we refer to [28] and propose a modified low bandwidth sub-Nyquist sampling receiving scheme employing RF sharing as shown in Fig. 1. In this architecture, only one high-speed RF device is required at the receiver end, which will be shared by all groups at an average cost. In addition, the shaping delays of different groups can also be synchronized effectively for the RF sharing architecture.
Fig. 1. The architecture of modified low-bandwidth sub-Nyquist sampling receiving scheme employing RF sharing.
2.2 Improved optical shaping
Different optical shaping pulses studied in [25] have different distributions of harmonic components, which will result in the transmitted sub-carriers aliasing at the low-frequency band with different weights. It means that the high-frequency sub-carriers have additional attenuation compared to the low-frequency sub-carriers. According to some research on MZM [29,30], it is usually compensated by inverting the nonlinear cosine transfer function of MZM, which is called arcsine digital pre-distortion (DPD) technology. Therefore, we propose a DPD optical pulse shaping scheme that has the same amplitude of harmonic components as the traditional scheme. The principle is as follows: when the MZM operates in Push-Pull, the field output expression of MZM can be expressed as:
where ${E_{in}}(t)$ and ${E_{out}}(t)$ are input and output optical field, ${V_\pi }$ is the half-wave voltage of the modulator, $u(t)$ represents the total voltage applied to the modulator and can be written as: where ${V_{bias}}$ represents the DC bias voltage of the modulator and $f(t)$ is the expression of the input electrical signal. According to the previous discussion, if the harmonic components of the optical shaping pulse have the same amplitude, the performance of low-bandwidth DDM scheme will be improved. Assuming that the modulator is biased at the quadrature point, the ideal input electrical signal can be expressed as:In the actual experiment, the DPD shaping pulse is firstly generated according to Eq. (9). As shown in Fig. 2, the time domain waveform and electrical frequency domain diagram of the DPD shaping pulse are measured by the experimental setup of Fig. 3 in Section 3. The frequency resolution of Fig. 2(b) is about 78.4 MHz. Then, the modulator is initially set at the quadrature point. Because the half-wave voltage of the modulator and the actual input voltage of MZM may deviate from the ideal setting, it needs to adjust the DC bias voltage of MZM so that $u(t)$ can satisfy the requirement, which is verified in Section 3. Regarding hardware complexity, sinusoidal signal sources require circuits such as oscillators and phase-locked loops (PLLs), and the generation of DPD shaping is based on direct digital synthesizer (DDS) technology. But the cost and complexity of the DPD shaping will be shared among all groups.
Fig. 3. Experimental setup. Insets (a), (d), and (e) are the DSP blocks of the system. (b) Optical spectrum of 12.5 GHz transmitted signal. (c) Optical spectrum of aliasing signal before and after OBPF.
3. Experimental setup
Figure 3 shows the experimental setup of the modified low-bandwidth DDM system. The insets (a), (d) and (e) are the DSP blocks of the proposed system. In this proof-of-concept experiment, the Nyquist sampling rate is 25 GSa/s and the number of groups is 4 (i.e., M = 4), which signifies that the sub-Nyquist sampling rate is 6.25 GSa/s. In the transmitter, the pseudo-random bit sequence (PRBS) is mapped into 16-QAM. Then the transmitter preprocesses the signal based on the aggregated channel response which is obtained in advance through 10 TSs for each frequency zone. To satisfy that the data output is a real number, a Hermitian conjugate symmetric structure is required to be constructed before IFFT. The IFFT size is 512 and the length of cyclic prefix (CP) is 16. Each frame has 10 TSs and 110 data-carrying OFDM symbols. The net rate of each group is 11.113 Gb/s, and the rate of aggregated OFDM signal is about 44.45 Gb/s. The signal generated offline is uploaded into an 80-Gsa/s sampling rate Fujitsu DAC with 16.7 GHz 3-dB bandwidth and a physical/effective number of bits of 8/6. Then it is boosted by a 30 GHz electrical amplifier (EA) with 20 dB gain. The amplified electrical signal is loaded to an MZM to generate the optical 12.5 GHz preprocessed signal whose optical spectrum is shown in Fig. 3(b). The spectral resolution is 0.02 nm. Finally, the optical signal is transmitted to the SSMF link with a fixed launch power of 9 dBm.
At the receiver end, the optical shaping module is realized by another Fujitsu FTM7938EZ MZM with a bandwidth of 25 GHz. The designed shaping pulse is generated by the above DAC and amplified by a 23 dB gain EA. Thus, in this proof-of-concept experiment, the clocks of signal modulation module and the optical shaping module are synchronized by using a multi-channel DAC. In actual deployment, the frequency offset between the two modules will affect the signal-to-noise ratio (SNR) of the system. According to [21], this problem can be solved by assigning different training symbols to different groups, which is expected to be verified in future research work. Due to insufficient experimental conditions, instead of using 4 MZM for experimental verification, we use one MZM and change the shaping delay to carry out the equivalent experiment. An Erbium-doped fiber amplifier (EDFA) is inserted after the optical shaping module. Besides, the signal is filtered by an OBPF with the 3-dB bandwidth of 6.25 GHz, which is mainly used to suppress SSBI introduced by optical shaping pulse harmonics. The optical spectrum of aliasing signal before and after OBPF is shown in Fig. 3(c). It has verified that the proposed scheme can achieve the same amplitude of harmonic components. Additionally, a variable optical attenuator (VOA) is used to control the received optical power (ROP) and the photodiode (PD) is applied to detect the signal. Instead of using an ADC with a sub-Nyquist sampling rate, the received electrical signal is captured by a Lecroy oscilloscope with an oversampling rate of 80 GSa/s, which sets a 4 GHz bandwidth limit completed by a Brick-Wall filter for the low-bandwidth cases. The offline DSPs are completed in MATLAB, including sub-Nyquist sampling, and conventional process of OFDM demodulation, where the FFT size of each group is reduced to N/M.
4. Results and discussion
Firstly, we study how the DPD shaping scheme can achieve the best shaping effect. We define the case where the bi coefficient in Eq. (9) are all set to 1 as without pre-emphasis. As shown in Fig. 4(a), due to the bandwidth limitation of the device, there is a roll-off of the higher harmonics of the signal without pre-emphasis. At this time, the bi coefficient can be set correspondingly according to the attenuation situation to realize pre-emphasis. Figure 4(b) shows measured magnitude responses of the different transmission schemes. It should be noted that the whole channel response is estimated by transmitting 4 different TSs sequentially. The subcarriers of these TSs are only localized in corresponding frequency zones and can be measured within 3.125 GHz after the aliasing caused by sub-Nyquist sampling [31].
Fig. 4. (a) Optical spectrum of different shaping pulse schemes. (b) Magnitude responses of different schemes. (c) Measured BER performance of different schemes versus ROP.
The aliasing performance with different 3-dB bandwidths of OBPF in DPD shaping scheme is also investigated and shown in Fig. 4(b). The bandwidth setting of OBPF will affect the aliasing effect because the harmonics of the shaping pulse will bring beat frequency interference. Additionally, the poor filtering effect will also lead to a spectrum notch. When the 3-dB bandwidth of OBPF is 6.25 GHz, the system with pre-emphasis can obtain a better degree of aliasing, and the condition number of ${\bf H}$ is 3.24. In contrast, when the 3-dB bandwidth is set to 12.5 GHz, the SSBI leads to a relatively rapid drop in the amplitude response and the condition number of this system is 5.12, which means that the scheme is more sensitive to noise than the previous one [27]. Moreover, we have added the comparison with and without DPD shaping in Fig. 4. Without DPD shaping scheme refers to generating optical pulses using a 6.25 GHz sin wave [25]. Figures 4(a) and (b) clearly show that DPD shaping is conducive to obtaining the required harmonic components, which can achieve better aliasing performance. The BER performance versus ROP of the above schemes is measured and plotted in Fig. 4(c). The scheme without DPD shaping has the worst reception sensitivity at the HD-FEC threshold. In contrast, the DPD shaping scheme with pre-emphasis and OBPF bandwidth of 6.25 GHz achieves the best transmission performance, which is verified again that a flatter estimated channel response is beneficial to system. In the following discussion, low-bandwidth DDM schemes adopt the best transmission conditions.
Then, the modified scheme is compared with the traditional high-bandwidth (BW) scheme. In the high BW schemes, the oscilloscope does not set the bandwidth limit of 4 GHz. Figure 5(a) shows measured magnitude responses of the different transmission schemes. In the low BW without shaping scheme, high-frequency subcarriers cannot transmit data due to bandwidth limitation. For the case of low BW with DPD shaping, the effective bandwidth of the preprocessed signal will be converted to 1/4 due to spectrum aliasing, which can effectively alleviate the analog bandwidth of receiver (including PD and oscilloscope). Therefore, the low BW with DPD shaping scheme shows the highest magnitude responses as shown in Fig. 5(a). Based on the discussion above, the harmonic powers of the DPD shaping scheme are the same, so the aliasing degree of each frequency band is the same, and the difference in magnitude responses of each zone is attributed to the uneven frequency response of the transmitter.
Fig. 5. (a) Magnitude responses of different transmission scheme. (b) Measured BER performance versus ROP. (c) SNR of different groups at the ROP of −11 dBm.
The BER performance versus ROP of different schemes is measured and plotted in Fig. 5(b). Additionally, this BER result is the average of all groups. As discussed earlier, low BW without shaping scheme cannot transmit data due to the bandwidth limitation of receiver. With the help of DPD shaping, the modified low-bandwidth DDM scheme can achieve about 1 dB receiver sensitivity improvement compared with the traditional high-bandwidth scheme at the HD-FEC threshold after optical back-to-back (OBTB) transmission. Compared with the OBTB scheme, the proposed low-bandwidth DDM system can successfully transmit 10.2 km SSMF with a receiver sensitivity about 0.4 dB higher than the traditional scheme at the HD-FEC threshold. In practice, when the transmission delay changes, the channel estimation can be carried out again to solve the problem. At the ROP of −11 dBm, the SNR performance of different groups is also investigated, as shown in Fig. 5(c). Different groups have similar SNR performance, verifying the practical feasibility of the proposed DDM scheme.
5. Conclusion
In this paper, we have experimentally demonstrated a costly and flexible 12.5-GHz/44.45-Gb/s DDM-based OFDM system employing low-bandwidth (3.125 GHz) and sub-Nyquist sampling rate (6.25 GSa/s) ADC. The proposed novel delay multiplexing method allows different groups to receive the desired data by only controlling the delay of the shaping module, which reduces the complexity of the scheme. With the help of DPD shaping, the proposed scheme can not only effectively achieve low-bandwidth reception but also acquires the same aliasing effect as the traditional high-BW scheme. In addition, the proposed scheme can also achieve about 0.4 dB receiver sensitivity improvement compared with the traditional high-BW DDM scheme at the HD-FEC threshold after 10.2 km SSMF transmission. As for the cost of system, the proposed RF sharing architecture requires only one high-speed device, which will be shared by all groups at an average cost. For the rest of the optical shaping module, MZM and OBPF can be designed by microring resonator which is expected to achieve low-cost and low-power photonic integration [32,33]. Consequently, the proposed low-bandwidth sub-Nyquist sampling receiving scheme enabled by DPD shaping is one of the most promising schemes for providing large transmission capacity to P2MP networks cost-efficiently.
Funding
Key-Area Research and Development Program of Guangdong Province (2020B0101080002); National Natural Science Foundation of China (U2001601, 61871408); Local Innovation and Research Teams Project of Guangdong Pearl River Talents Program (2017BT01X121); Fundamental and Applied Basic Research Project of Guangzhou City (202002030326); Open Fund of IPOC (BUPT) (IPOC2020A010).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
References
1. J. Kani, F. Bourgart, A. Cui, A. Rafel, M. Campbell, R. Davey, and S. Rodrigues, “Next-generation PON Part I: Technology roadmap and general requirements,” IEEE Commun. Mag. 47(11), 43–49 (2009). [CrossRef]
2. N. Cvijetic, D. Qian, and J. Hu, “100 Gb/s optical access based on optical orthogonal frequency-division multiplexing,” IEEE Commun. Mag. 48(7), 70–77 (2010). [CrossRef]
3. M. Chen, L. Zhang, D. Xi, G. Liu, H. Zhou, and Q. Chen, “Experimental Demonstration of DFT-Precoded Guard-Band OSSB-OFDM Signal Reception With ADC Undersampling Technique,” in IEEE Access, vol. 8, pp. 16838–16845, (2020).
4. Z. Li, W. Wang, D. Zou, F. Li, J. Li, Q. Sui, and Z. Li, “DFT Spread Spectrally Efficient Frequency Division Multiplexing for IM-DD Transmission in C-Band,” J. Lightwave Technol. 38(13), 3526–3532 (2020). [CrossRef]
5. Q. Zhang, N. Stojanovic, C. Prodaniuc, C. Xie, M. Koenigsmann, and P. Laskowski, “Single-lane 180 Gbit/s PAM-4 signal transmission over 2-km SSMF for short-reach applications,” Opt. Lett. 41(19), 4449–4452 (2016). [CrossRef]
6. F. Li, X. Li, J. Yu, and C. Lin, “Optimization of training sequence for DFT-Spread DMT signal in optical access network with direct detection utilizing DML,” Opt. Express 22(19), 22962–22967 (2014). [CrossRef]
7. M. Chen, L. Wang, D. Xi, L. Zhang, H. Zhou, and Q. Chen, “Comparison of Different Precoding Techniques for Unbalanced Impairments Compensation in Short-Reach DMT Transmission Systems,” J. Lightw. Technol. 38(22), 6202–6213 (2020). [CrossRef]
8. J. Shi, J. Zhang, N. Chi, and J. Yu, “Comparison of 100G PAM-8 CAP-64 and DFT-S OFDM with a bandwidth-limited direct detection receiver,” Opt. Express 25(26), 32254–32262 (2017). [CrossRef]
9. F. Li, J. Yu, Z. Cao, J. Zhang, M. Chen, and X. Li, “Experimental Demonstration of Four-Channel WDM 560 Gbit/s 128QAM-DMT Using IM/DD for 2-km Optical Interconnect,” J. Lightwave Technol. 35(4), 941–948 (2017). [CrossRef]
10. M. Chen, H. Zhou, Z. Zheng, R. Deng, Q. Chen, M. Peng, C. Liu, J. He, L. Chen, and X. Tang, “OLT-centralized sampling frequency offset compensation scheme for OFDM-PON,” Opt. Express 25(16), 19508–19516 (2017). [CrossRef]
11. Y. Li, J. Han, and X. Zhao, “Performance investigation of DFT-spread OFDM signal for short reach communication systems beyond NG-PON2,” IEEE Access 7, 27426–27431 (2019). [CrossRef]
12. P. -H. Ting, S. -H. Yu, Z. -W. Huang, C. -C. Wei, S. Chi, and C. -T. Lin, “Fronthaul Optical Links Implemented by Using Sub-Nyquist Sampling Rate ADC for B5G/6G Sub-THz Ma-MIMO Beamforming,” 2021 Optical Fiber Communications Conference and Exhibition (OFC) (2021), pp. 1–3.
13. H.-C. Liu, Chi-Hsia Lin, C.-T. Lin, C.-C. Wei, H.-T. Huang, H.-H. Hsu, M.-F. Wu, and S. Chi, “Simple receiving scheme in 100-GHz DD OFDM RoF systems employing low-sampling-rate ADCs and digital preprocess,” presented at Optical Fiber Communications Conf. (2015), paper Th2A.7.
14. Y C. Wei, H. Liu, and C. Lin, “Novel delay-division-multiplexing OFDMA passive optical networks enabling low-sampling-rate ADC,” in Proc. OFC (2015), pp. 1–3.
15. R. P. Giddings, E. Hugues-Salas, and J. M. Tang, “Experimental demonstration of record high 19.125 Gb/s real-time end-to-end dual-band optical OFDM transmission over 25 km SMF in a simple EML-based IMDD system,” Opt. Express 20(18), 20666–20679 (2012). [CrossRef]
16. Q. W. Zhang, E. Hugues-Salas, R. P. Giddings, M. Wang, and J. M. Tang, “Experimental demonstrations of record high REAM intensity modulator-enabled 19.25Gb/s real-time end-to-end dual-band optical OFDM colorless transmissions over 25 km SSMF IMDD systems,” Opt. Express 21(7), 9167–9179 (2013). [CrossRef]
17. Q. W. Zhang, E. Hugues-Salas, Y. Ling, H. B. Zhang, R. P. Giddings, J. J. Zhang, M. Wang, and J. M. Tang, “Record-high and robust 17.125 Gb/s gross-rate over 25 km SSMF transmissions of real-time dual-band optical OFDM signals directly modulated by 1 GHz RSOAs,” Opt. Express 22(6), 6339–6348 (2014). [CrossRef]
18. R. Deng, J. He, J. Yu, Y. Wei, X. Xiao, K. Lv, X. Xin, and G.-K. Chang, “Increasing data rate of an optical IMDD system using a cost-efficient dual-band transmission scheme based on RTZ DAC and sub-Nyquist sampling ADC,” Opt. Express 26(9), 11599–11607 (2018). [CrossRef]
19. L. Cheng, H. Wen, X. Zheng, H. Zhang, and Y. Guo, “Predistortion of high speed optical OFDM signal for aliasing-free receiving in multiple low-bandwidth receiver system,” Chin. Opt. Lett. 8(4), 377–380 (2010). [CrossRef]
20. L. Cheng, H. Wen, X. Zheng, H. Zhang, and B. Zhou, “Channel characteristic division OFDM-PON for next generation optical access,” Opt. Express 19(20), 19129–19134 (2011). [CrossRef]
21. C. Wei, H. Liu, C. Lin, and S. Chi, “Analog-to-Digital Conversion Using Sub-Nyquist Sampling Rate in Flexible Delay-Division Multiplexing OFDMA PONs,” J. Lightwave Technol. 34(10), 2381–2390 (2016). [CrossRef]
22. G. Bai, Y. Jiang, L. Hu, J. Tian, and Y. Zi, “Delay division multiplexing orthogonal frequency-division multiple access passive optical networks using low-sampling-rate analog-to-digital converter,” Acta Phys. Sin. 66(19), 194204 (2017). [CrossRef]
23. J. Hsu, M. Yu, C. Wei, C. Lin, F. Liu, L. Zhou, and L. Fang, “Employing Hybrid sub-Nyquist Sampling Rates to Support Heterogeneous Services of Varying Capacity in 25-Gbps DDM-OFDM-PON,” IEEE Photonics J. 10(2), 1–8 (2018). [CrossRef]
24. C. H. Lin, R. Fang, C. T. Lin, C. C. Wei, and S. Chi, “43.63-Gbit/s multiple-user SC-FDMA PON with sub-Nyquist receiver and PAPR reduction,” IEEE Photonics Technol. Lett. 30(19), 1663–1666 (2018). [CrossRef]
25. W. Chen, M. Yu, L. Yang, C. Wei, and C. Lin, “Low-Bandwidth Sub-Nyquist A/D Conversion in Delay-Division Multiplexing OFDM PONs Enabled by Optical Shaping,” Optical Fiber Communications Conference and Exhibition (OFC) (2020), pp. 1–3.
26. Z. Luo, M. Yin, X. Yi, Z. Li, and F. Li, “Improved Delay-Division Multiplexing OFDM-PON Scheme Employing Low-Bandwidth Sub-Nyquist Sampling-Rate ADC,” in Proc. Asia Commu. Photon. Conf. (2021), T4A.85.
27. L. Cheng, H. Wen, X. Zheng, H. Zhang, Y. Guo, and B. Zhou, “A Low-Speed Receiving Method in Broadband Optical OFDM System,” IEEE Photonics Technol. Lett. 22(15), 1165–1167 (2010). [CrossRef]
28. T. Schneider, G. Raoof Mehrpoor, and S. Preussler, “Frequency-time coherence for all-optical sampling without optical pulse source,” Sci. Rep. 6(1), 34500 (2016). [CrossRef]
29. A. Napoli, M. M. Mezghanni, S. Calabrò, R. Palmer, G. Saathoff, and B. Spinnler, “Digital Predistortion Techniques for Finite Extinction Ratio IQ Mach–Zehnder Modulators,” J. Lightwave Technol. 35(19), 4289–4296 (2017). [CrossRef]
30. G. Paryanti and D. Sadot, “Predistortion of Mach–Zehnder Modulator Using Symmetric Imbalance,” J. Lightwave Technol. 35(13), 2757–2768 (2017). [CrossRef]
31. J.-H. Hsu, M. Yu, F. Liu, C.-H. Lin, C.-T. Lin, L. Zhou, L. Fang, and C.-C. Wei, “On channel estimation schemes for APD-based DDM-OFDM-PONs under sub-Nyquist sampling,” Opt. Express 26(18), 23808–23818 (2018). [CrossRef]
32. Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, “Micrometre-scale silicon electro-optic modulator,” Nature 435(7040), 325–327 (2005). [CrossRef]
33. H. Jiang, L. Yan, and D. Marpaung, “Chip-based arbitrary radio-frequency photonic filter with algorithm-driven reconfigurable resolution,” Opt. Lett. 43(3), 415–418 (2018). [CrossRef]
